Search block can't change appearance if inside navigation block

[tomxygen]

Description

It's not possible to change the appearance of the search button if it is placed inside the navigation block.

Step-by-step reproduction instructions

1. open the Site editor
2. Go to Pages > Home
3. Edit the header and add navigation block
4. inside the navigation block, place a search block
5. Try to edit the appearance, like setting it as a button only.
   The edit will not be applied and will be reverted to the original settings.

If instead of editing it from Pages > Home, you go to Library > Header, the issue isn't there.

Screenshots, screen recording, code snippet

See attached video.

videowp.mov

Environment info

No response

Please confirm that you have searched existing issues in the repo.

Yes

Please confirm that you have tested with all plugins deactivated except Gutenberg.

Yes

[t-hamano]

Thanks for the report.

I was able to reproduce this problem with Twenty Twenty theme and the latest Gutenberg trunk.

e51ded3cbb5641d5e2c41b2dfab1e0f6.mp4

[ndiego]

I was also able to confirm, but I wanted to note that this issue also seems to appear in 6.2.

[annezazu]

cc @scruffian as a heads up.